Principles of Organic Chemistry
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Bonding Models
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Fact: electrons hold molecules together.
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Theories: more than one way to conceptualize bonding. Let’s follow Carroll in the
consideration of two theories of bonding.
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Before we try to wrap our minds around the molecular orbitals of methane let’s
play with some other molecular orbitals.
The author spends some time discussing the difference between MO theory and Valence Bond
theory.
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In one case MO theory we are taking about electron energies and populations around
molecules.
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lecture 5, page 1
Put the nuclei and throw the electrons at them.
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In the other case VB theory, we are talking about the energetic and population changes that
occur when atoms with their core and valence electrons around them form bonds with
between themselves.
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Let’s discuss electrons in terms of molecular orbitals (MOs) and atomic orbitals (AOs).
In your chemical education you have more than likely been exposed to valence shell electron pair
repulsion (VSEPR) theory.
N
H
H
H
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P
H
H
H
Prediction of the bond angles of ammonia and phosphine are problematic for VSEPR.
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That of ammonia is 107.3°. The structure is dynamic at room temperature
undergoing fast inversion.
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The bond angle of phosphine is 93.7° (Cotton, Wilkinson, Murillo, and
Bochmann in Advanced Inorganic Chemistry 6th ed. p 388)
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What makes the lone pair on the phosphorus atom any bigger (more repulsive)
than those on the nitrogen atom?
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It might have made just as much sense to argue that PH3 should flatter
than NH3 because the lone pair is further away from the nucleus and
should thus affect the bonded H atoms to a lesser extent than in NH3.
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However we can talk very sensibly about the geometry of the hydrides of
N and P on the basis of hybridization and bond strength.
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The bonds are stronger when both species (N and P) are flat. But electron
repulsion is also greatest in the planar geometry.*
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The flat structures are sp2 hybrids. There is a p-orbital with a
lone pair in it.
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Ammonia has a wider bond angle and is closer in energy to its
flat transition state because its bonds are optimized by better
overlap.
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Overlap between principle quantum number 1 and 2
occurs in NH3 whereas in PH3, overlap occurs between
principle quantum number 1 and 3.
* From S.F.A. Kettle, “Symmetry and Structure, Readable Group Theory for
Principles of Organic Chemistry
lecture 5, page 2
Chemists” p 6-7.
The potential energy barrier for the inversion is equal to the difference in total energy
between the ammonia molecule in its normal, pyramidal, shape and the planar
configuration. In order to obtain a theoretical value for this barrier, Clementi carried
out rather detailed calculations for each geometry. The results were very surprising.
They showed that the N-H bonding is greater in the planar molecule—there is a loss of
bonding of N-H bonding energy of approximately 7.0 x 102 kJ mole-1 (167 kcal mole-1)
in going from the planar to the pyramidal geometry; this loss is accompanied by a
slight lengthening of the N-H bond. Bonding favours a planar ammonia molecule. A
comparison of the most stable pyramidal and most stable planar geometries shows that
the electron-electron and nuclear-nuclear repulsion energies favour the pyramidal
molecule over the planar by about 7.2 x 102 kJ mole-1 (172 kcal mole-1). Repulsive
forces favour a pyramidal molecule. Note the way that the bonding and repulsive
energy changes between the two shapes almost exactly cancel each other. It is the
slight dominance of the repulsive forces by 20 kJ mole-1 (5 kcal mole-1) which leads to
the equilibrium geometry of the ammonia molecule in its electronic ground state being
pyramidal.
We are left with a most disturbing situation. There is no doubt that the strongest N-H
bonding in the ammonia molecule is to be found when it is planar yet two of the simple
models considered earlier in this chapter explained its geometry by the assumption
that this bonding is a maximum in the pyramidal molecule! Similarly, the models
based on electron-electron repulsion ignored both the fact that nuclear-nuclear
repulsion is of comparable importance and the fact that their sum is almost exactly
cancelled by changes in the bonding energy. This would not matter so much if there
were some assurance that repulsive energies would outweigh the bonding in all
molecules (molecular geometries could then reliably be explained using a
repulsion-based argument). Unfortunately, no such general assurance can be given.
This can be seen if the discussion of the ammonia molecule is extended to include
some related species.
The molecules NH3, PH3, NH2F, PH2F, NHF2 PHF2 NF3, and PF3 all have similar,
pyramidal, structures and would be treated similarly in all simple models. But
calculations by Schmiedekamp and co-workers6 have shown that the first four owe
their pyramidal geometry to the dominance of repulsive forces (bonding is stronger
when they are planar) but the last four are pyramidal because the bonding is greatest in
this configuration and dominates the repulsive forces.
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The take home message is that the sweeping generalizations that you learned in Chem I and
Organic I do not reflect reality that well.
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The universe is not that simple. Nature challenges us when ever we examine it
with intentions to explain it.
With the caveat that your last learned paradigm was flawed let’s look at MO theory as a paradigm to
explain the behavior of electrons in molecules.
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Let’s start off by being a bit honest. An MO is a mathematical equation that does its best to
describe the behavior of electrons in molecules.
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If an electron would behave like a particle at all velocities we could treat collections of
electrons, protons and neutrons with classical Newtonian mechanics.
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It is not reality; it is a model of reality.
They don’t; they behave like waves most of the time.
A few principles of MO theory, the LCAO method.
Principles of Organic Chemistry
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lecture 5, page 3
AOs combine to make an MO via linear combinations.
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The number of these orbitals is conserved.
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#AOs = #MOs
MOs are space around the molecule in which electrons have a high probability of
occupation.
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This space // is conserved.
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example
C C O
C C C
pi MOs of Allyl anion
pi MOs of an enolate
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The diagram above was adapted from Ian Fleming,
“Frontier Orbitals and Organic Chemical Reactions”
J. Wiley, 1978.
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The all carbon structure is electronically symmetric
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The O in the enolate hogs orbital space in MO1.
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C-C bond order decreases and C-O bonding
increases.
In the homo C-C bond order increases.
Let’s mess with hydrogen to keep things as simple as possible.
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We will also ignore the coefficients (the relative sizes of the orbitals) also to keep things
simple.
H
a hydrogen s orbital.
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An electron in this orbital has a certain energy and this can be represented by an
orbital energy diagram.
Electrons behave like waves and waves have phase.
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When there is only one orbital in the picture the phase does not matter.
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Only when the orbital interacts with another orbital can we have two
possible combinations.
Principles of Organic Chemistry
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H
H
H
H
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The lower combination is the bonding combination (molecular orbital). The upper
combination is the antibonding combination (molecular orbital).
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The same-phase combination makes it advantageous for electrons to occupy it
because it has less energy than the upper combination.
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H
H
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We say that the upper orbital contains a node, a plane or a volume that
electrons do not occupy.
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The orbital with the node is high-energy when occupied by electrons.
These are the only possible phase combinations of two orbitals. Shall we do
three?
H
H
H H
H
H
H
A
+
H
lecture 5, page 4
H
H
H
C
H
H
H
B
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H
D
These are all possible combinations of three orbitals.
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You will notice that B has no nodes.
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Thus, by analogy to what was said above, it is lowest in energy.
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However A has two nodes. That is the phase changes two times as we go from one
end of the molecule to the other.
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If symmetry is beautiful orbitals C and D are ugly little things.
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A and B have two axes of symmetry but C and D only have one.
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Furthermore C and D should be degenerate (possessing the same
energy).
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Let’s take a closer look at C and D.
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C and D are different from A and B by another characteristic.
Where as there is no way to convert A to B by an operator that
changes the phase.
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Multiplication by -1
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C and D can be converted to one another by multiplication by
-1.
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C and D are called reducible representations. We can get to an
irreducible representation by combining C and D.
Principles of Organic Chemistry
C+D=
H
H
lecture 5, page 5
H
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The last molecular orbital that we generated in the list is called a non-bonding MO.
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A molecular orbital energy diagram will show you why it is not beneficial for H3 to form.
anti-bonding
energy
non-bonding
0
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We will take a closer look at how to calculate these coefficients and what the
nature of the φs is.
Take a look at the bonding description of XeF2 in your reading assignment (J. Chem. Ed.
1977, 54, 590-595.)
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Note how the atomic orbitals in the diagram that transform to become molecular
orbitals are remarkably similar to the H3 and the allyl example above.
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Ψ2 = c21φ21 - c23φ23
Ψ1 = c11φ11 + c12φ12 + c13φ13
bonding
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Ψ3 = c31φ31 - c32φ32 + c33φ33
All examples have bonding, non-bonding and antibonding orbitals.
A bonding Model of CH4.
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It certainly is logical to consider the simplest alkane.
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If you can’t understand methane what can you understand?
The Organic I explanation goes as follows.
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Methane is composed of atomic s and p orbitals of principle quantum number 2.
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There are three p orbitals and one s orbital.
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to explore space equally these orbitals are mixed to produce four
identical sp3 orbitals.
The H atoms are held by electrons that borrow spatial character from all three
Cartesian coordinates.
z
x
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y
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bond vectors:
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<1,1,1>, <−1, −1, 1>, <−1, 1, −1>, <1, −1, −1>
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cos(a) = u•v/(|u|||v|)
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cos(a) = (−1−1+1)/[(√12+12+12)(√12+12+12)] = −1/3
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a = 109.47122 . . .